Fabrizio Zanello, Ph.D.
Books and
Monographs
Publications in
Refereed
Journals
Bibliography
1. (with M. Boij, J. Migliore, R. Mirò-Roig and U. Nagel) “On the shape of a pure Osequence”, Mem. Amer. Math. Soc. 218 (2012), no. 1024, vii + 78 pp.. ISBN-10:
0-8218-6910-8; ISBN-13: 978-0-8218-6910-9
1. I numeri di Fermat, Periodico di Matematiche, VII, 5 (1998), no. 2-3, 63–68
2. Some observations on the statistical independence and the distribution of zeros in
the Selberg Class, Rend. Circ. Mat. Palermo (2), 52 (2003), no. 2, 211–223
3. Extending the idea of compressed algebra to arbitrary socle-vectors, J. Algebra 270
(2003), no. 1, 181–198
4. When are There Infinitely Many Irreducible Elements in a Principal Ideal Domain?,
Amer. Math. Monthly 111 (2004), no. 2, 150–152
5. Extending the idea of compressed algebra to arbitrary socle-vectors, II: cases of nonexistence, J. Algebra 275 (2004), no. 2, 730–748
6. Stanley’s theorem on codimension 3 Gorenstein h-vectors, Proc. Amer. Math. Soc.
134 (2006), no. 1, 5–8
7. Level algebras of type 2, Comm. Algebra 34 (2006), no. 2, 691–714
8. When is there a unique socle-vector associated to a given h-vector?, Comm. Algebra
34 (2006), no. 5, 1847–1860
9. A non-unimodal codimension 3 level h-vector, J. Algebra 305 (2006), no. 2, 949–956
10. Improving the bounds of the Multiplicity Conjecture: the codimension 3 level case,
J. Pure Appl. Algebra 209 (2007), no. 1, 79–89
11. Partial derivatives of a generic subspace of a vector space of forms: quotients of
level algebras of arbitrary type, Trans. Amer. Math. Soc. 359 (2007), no. 6,
2675–2686
12. (with J. Migliore) The Hilbert functions which force the Weak Lefschetz Property,
J. Pure Appl. Algebra 210 (2007), no. 2, 465–471
13. The h-vector of a relatively compressed level algebra, Comm. Algebra 35 (2007),
no. 4, 1087–1091
14. (with M. Boij) Level Algebras with Bad Properties, Proc. Amer. Math. Soc. 135
(2007), no. 9, 2713–2722
15. (with J. Migliore and U. Nagel) An improved Multiplicity Conjecture for codimension three Gorenstein algebras, Comm. Algebra 36 (2008), no. 1, 112–119
16. (with J. Migliore and U. Nagel) A characterization of Gorenstein Hilbert functions
in codimension four with small initial degree, Math. Res. Lett. 15 (2008), no. 2,
331–349
17. (with J. Migliore and U. Nagel) On the degree two entry of a Gorenstein h-vector
and a conjecture of Stanley, Proc. Amer. Math. Soc. 136 (2008), no. 8, 2755–2762
18. (with J. Migliore) The strength of the Weak Lefschetz Property, Illinois J. Math.
52 (2008), no. 4, 1417–1433
19. (with J. Migliore and U. Nagel) Bounds and asymptotic minimal growth for Gorenstein Hilbert functions, J. Algebra 321 (2009), no. 5, 1510–1521
20. (with J. Zylinski) Forcing the Strong Lefschetz and the Maximal Rank Properties,
J. Pure Appl. Algebra 213 (2009), no. 6, 1026–1030
21. Interval Conjectures for level Hilbert functions, J. Algebra 321 (2009), no. 10,
2705–2715
22. (with M. Boij) Some algebraic consequences of Green’s hyperplane restriction theorems, J. Pure Appl. Algebra 214 (2010), no. 7, 1263–1270
23. (with A. Van Tuyl) Simplicial complexes and Macaulay’s inverse systems, Math.
Z. 265 (2010), no. 1, 151–160
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24. (with J. Li) Monomial Complete Intersections, The Weak Lefschetz Property and
Plane Partitions, Discrete Math. 310 (2010), no. 24, 3558–3570
25. The KOH terms and classes of unimodal N -modular diagrams, J. Combin. Theory
Ser. A 118 (2011), no. 8, 2498–2510
26. (with R.P. Stanley) On the rank function of a differential poset, Electron. J. Combin. 19 (2012), no. 2, P13, 17 pp.
27. (with C. Sandon) Warnaar’s bijection and colored partition identities, I, J. Combin.
Theory Ser. A 120 (2013), no. 1, 28–38
28. (with T. Hà and E. Stokes) Pure O-sequences and matroid h-vectors, Ann. Comb.
17 (2013), no. 3, 495–508
29. (with C. Sandon) Warnaar’s bijection and colored partition identities, II, Ramanujan J. 33 (2014), no. 1, 83–120
30. (with M. Boij, J. Migliore, R. Mirò-Roig and U. Nagel) On the Weak Lefschetz
Property for artinian Gorenstein algebras of codimension three, J. Algebra 403
(2014), no. 1, 48–68
31. (with A. Pastine) Two unfortunate properties of pure f -vectors, Proc. Amer. Math.
Soc. 143 (2015), no. 3, 955–964
32. On the number of odd values of the Klein j-function and the cubic partition function, J. Number Theory 151 (2015), 107–115
33. (with R.P. Stanley) The Catalan case of Armstrong’s conjecture on simultaneous
core partitions, SIAM J. Discrete Math. 29 (2015), no. 1, 658–666
34. Zeilberger’s KOH theorem and the strict unimodality of q-binomial coefficients,
Proc. Amer. Math. Soc. 143 (2015), no. 7, 2795–2799
35. (with R.P. Stanley) Unimodality of partitions with distinct parts inside Ferrers
shapes, European J. Combin. 49 (2015), 194–202
36. (with D. Cook II, J. Migliore and U. Nagel) An algebraic approach to finite projective planes, J. Algebraic Combin. 43 (2016), no. 3, 495–519
37. (with R.P. Stanley) Some asymptotic results on q-binomial coefficients, Ann. Comb.,
to appear. Available on the arXiv
Preprints
1. (with S.D. Judge and W.J. Keith) On the density of the odd values of the partition
function, preprint. Available on the arXiv
2. (with J. Migliore) Stanley’s nonunimodal Gorenstein h-vector is optimal, preprint.
Available on the arXiv
Invited Book
Chapters
Other
Publications
1. (with J. Migliore and U. Nagel) Pure O-sequences: known results, applications and
open problems, in: “Commutative Algebra. Expository Papers Dedicated to David
Eisenbud on the Occasion of His 65th Birthday” (I. Peeva, Ed.), Springer New YorkHeidelberg-Dordrecht-London, 715 pp. (2013)
1. “La Classe di Selberg: distribuzione statistica e zeri delle combinazioni lineari”,
M.S. Thesis, University of Genova, Italy (2001)
2. “H-vectors and socle-vectors of graded artinian algebras”, Ph.D. Thesis, Queen’s
University at Kingston, Canada (2004)
Fabrizio Zanello,
May 14, 2016
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